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Concept in logic
A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable
Substitution_(logic)
abstract machines, predicate logic, and symbolic computation. A simple example of a lambda calculus with explicit substitution is "λx", which adds one new
Explicit_substitution
Basic notion of sameness in mathematics
Z),} therefore X = Z . {\displaystyle X=Z.} Substitution: See Substitution (logic) § Proof of substitution in ZFC. Function application: Given a = b {\displaystyle
Equality_(mathematics)
1956 computer program written by Allen Newell, Herbert A. Simon and Cliff Shaw
form A → B {\displaystyle A\to B} after substitution. It then attempts to prove A {\displaystyle A} by substitution; if this fails, A {\displaystyle A} becomes
Logic_Theorist
In logic, a statement which is always true
propositional logic, or valid sentences of predicate logic that can be reduced to propositional tautologies by substitution. Propositional logic begins with
Tautology_(logic)
Type of logical system
first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified
First-order_logic
Topics referred to by the same term
up substitution in Wiktionary, the free dictionary. Substitution may refer to: Substitution (poetry), a variation in poetic scansion Substitution (theatre)
Substitution
Symbol representing a property or relation in logic
In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all.
Predicate_(logic)
Logical formalism using combinators instead of variables
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell
Combinatory_logic
Mathematical-logic system
evaluation of expressions in programming languages Explicit substitution – The theory of substitution, as used in β-reduction Harrop formula – A kind of constructive
Lambda_calculus
Study of correct reasoning
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical
Logic
Assignment of meaning to the symbols of a formal language
instead of quantifying over substitution instances. Some authors also admit propositional variables in first-order logic, which must then also be interpreted
Interpretation_(logic)
Branch of logic
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes
Propositional_logic
One of five systems of modal logic
In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic
S5_(modal_logic)
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Object-oriented programming principle
subtype of an immutable point, whereas Liskov substitution principle forbids this. Liskov substitution principle explains a property, "If for each object
Liskov_substitution_principle
Approach to logic
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to
Term_logic
Overview of and topical guide to thought
Reasoning Storytelling Stream of consciousness (psychology) Subconscious Substitution (logic) Suspicion (emotion) Theories Thinking processes (theory of constraints)
Outline_of_thought
System of formal deduction in logic
with a rule of substitution, as this article does. The use of "Hilbert-style" and similar terms to describe axiomatic proof systems in logic is due to the
Hilbert_system
Topics referred to by the same term
Substitution method may refer to: Substitution method (optical fiber), a way to calculate power loss in fiber optic cables Substitution method (optimization)
Substitution_method
List of symbols used to express logical relations
contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set
List_of_logic_symbols
Method of deriving conclusions
of deriving conclusions from premises. They are integral parts of formal logic, serving as the logical structure of valid arguments. If an argument with
Rule_of_inference
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India
History_of_logic
Mathematical model for deduction or proof systems
redirect targets Substitution instance – Concept in logicPages displaying short descriptions of redirect targets Theory (mathematical logic) – Set of sentences
Formal_system
Form of logic that allows quantification over predicates
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic
Second-order_logic
Algorithmic process of solving equations
V} . Then a substitution σ {\displaystyle \sigma } is subsumed by another substitution τ {\displaystyle \tau } if there is a substitution θ {\displaystyle
Unification (computer science)
Unification_(computer_science)
Inference seeking the simplest and most likely explanation
first-order logic, without requiring any preliminary reduction of formulae into normal forms. These methods have also been extended to modal logic. Abductive
Abductive_reasoning
System of formal mathematical logic
meaning that the substitution does not cause any occurrences of free variables of A to become bound in the result of the substitution. Axiom 1 expresses
Q0_(mathematical_logic)
substitution operations. The relationships between these algebraic systems form an important part of the theory of algebraic logic. Algebraic logic Cylindric
Polyadic_algebra
Branch of logic
showing what substitution of equals for equals is being used. This premise is theorem ( 3.9 ) {\textstyle (3.9)} with the substitution p := q {\textstyle
Equational_logic
Components of a mathematical or logical formula
e. if u = tσ for some renaming substitution σ. In that case, u is a renaming of t, too, since a renaming substitution σ has an inverse σ−1, and t = uσ−1
Term_(logic)
Inference rule in logic, proof theory, and automated theorem proving
(term). Unifying the two produces the substitution X ↦ a Discarding the unified predicates, and applying this substitution to the remaining predicates (just
Resolution_(logic)
3-volume treatise on mathematics, 1910–1913
occur in ƒ(φẑ) by the substitution of values of φ for p, q, r, ... in a [logical-] function, and, if φx ≡ ψx, the substitution of φx for p in a [logical-]
Principia_Mathematica
Statement that is taken to be true
{\displaystyle \phi } with the term t {\displaystyle t} substituted for x {\displaystyle x} . (See Substitution of variables.) In informal terms, this example
Axiom
System including an indeterminate value
three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which
Three-valued_logic
Non-contradiction of a theory
denotes the substitution of each x {\displaystyle x} in φ {\displaystyle \varphi } by a t {\displaystyle t} ; see also First-order logic.[citation needed]
Consistency
Argument whose conclusion must be true if its premises are
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true
Validity_(logic)
Impossible task in computing
Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced using
Entscheidungsproblem
Logical incompatibility between two or more propositions
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect
Contradiction
Application of logical methods to philosophical problems
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often
Philosophical_logic
Class of formal logics
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had
Classical_logic
Method in formal logic
rule of detachment." A substitution A that when applied to p {\displaystyle p} produces t {\displaystyle t} , and substitution B that when applied to
Condensed_detachment
School of thought in philosophy of mathematics
is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and
Logicism
Bearer of truth values
In some cases, it depends on the interpretation whether this type of substitution for propositional attitude reports is possible or not, such as the contrast
Proposition
Form of reasoning
invalid deductive reasoning is a form of deductive reasoning. Deductive logic studies under what conditions an argument is valid. According to the semantic
Deductive_reasoning
English economist and logician (1835–1882)
Pure Logic; or, the Logic of Quality apart from Quantity, Edward Stanford, London 1865. The Coal Question, Macmillan and Co. 1869. The Substitution of Similars
William_Stanley_Jevons
Characteristic of some logical systems
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can
Completeness_(logic)
Mathematical logic concept
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent
Contraposition
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
t[\sigma ]} . These operations are respectively called substitution in types and substitution in terms. Alternatively, this data can be packaged as a
Semantics_of_type_theory
Overview of and topical guide to logic
Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal
Outline_of_logic
Precisely specified semantic version of a statement
terms belong to logic, and not those given in concrete terms. The concrete terms man, mortal, and so forth are analogous to the substitution values of the
Logical_form
Study of the scope and nature of logic
Philosophy of logic is the branch of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as
Philosophy_of_logic
Various systems of symbolic logic
logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by
Intuitionistic_logic
Study of the semantics, or interpretations, of formal and natural languages
In logic, the semantics or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations of)
Semantics_(logic)
Variable that stores data about other variables or program structure
be substituted by different instances. Attempts to formalize the notion of metavariable result in some kind of type theory. Explicit substitution Hunter
Metavariable
Relationship where one statement follows from another
consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when
Logical_consequence
Mathematical use of "there exists"
In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually
Existential_quantification
Formal system of logic
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers
Higher-order_logic
Term in logic and deductive reasoning
In logic, soundness can refer to either a property of arguments or a property of formal deductive systems. An argument is sound if (and only if) it is
Soundness
Logical formulation of recursion
In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development
Fixed-point_logic
2011 video game
modes triggered by the Player Performance Evaluator, Minor League substitution logic improvements, advancement system improvements that now compares a
MLB_11:_The_Show
Syntactically correct logical formula
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence
Well-formed_formula
Logical principle
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is
Law_of_excluded_middle
Type of formal logic
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion
Paraconsistent_logic
Reasoning about equations with free variables
logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses
Algebraic_logic
Branch of logic
Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements)
Informal_logic
Formal language and associated computer program
based on variable substitution. The algorithm also has optional provisos for what variables must remain distinct after a substitution is made. Comments
Metamath
Logic theorem
In logic, the law of noncontradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction)
Law_of_noncontradiction
Diagram that shows all possible logical relations between a collection of sets
set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple
Venn_diagram
Hierarchical typed logic
speech" in the language of the logic reflect this typeful partitioning of the universe, even on the syntax level: substitution and argument passing can be
Many-sorted_logic
Kind of proof calculus
operation on proofs is the substitution of one proof for an assumption used in another proof. This is commonly known as a substitution theorem, and can be proved
Natural_deduction
Formal systems of logic that significantly differ from standard logical systems
Non-classical logics (sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional
Non-classical_logic
Standard system of axiomatic set theory
follows from the substitution property of equality. ZFC is constructed in first-order logic. Some formulations of first-order logic include identity;
Zermelo–Fraenkel_set_theory
Fundamental theorem in mathematical logic
theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem
Gödel's_completeness_theorem
Type of logical formula
mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form that gives it useful properties for use in logic programming
Horn_clause
Algebraic manipulation of "true" and "false"
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the
Boolean_algebra
Paradox in set theory
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician
Russell's_paradox
Situation in which one cannot avoid a problem because of contradictory constraints
marry a woman who is not a virgin. This closed logic loop clearly illustrated Catch-22 because by her logic, all men who refuse to marry her are sane and
Catch-22_(logic)
Mapping of mathematical formulas to a particular meaning
structures are the objects used to define the semantics of first-order logic, cf. also Tarski's theory of truth or Tarskian semantics. For a given theory
Structure (mathematical logic)
Structure_(mathematical_logic)
Whether a decision problem has an effective method to derive the answer
effectively determined. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. A theory (set of sentences
Decidability_(logic)
Mathematical theory of data types
judgmental equality define substitution for application of lambda terms list all the interactions of equality, such as substitution define a hierarchy of type
Type_theory
Symbolic logic system
Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson under the name "Minimalkalkül". It is a paraconsistent
Minimal_logic
aimed to express all of arithmetic in terms of logic. Frege's work laid the groundwork for much of modern logic and was highly influential, though it encountered
Mathematical_object
Theorem in mathematical logic
mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the strongest
Lindström's_theorem
Mathematical use of "for all" and "there exists"
In mathematical logic, quantifiers are formal counterparts of natural-language adjectives like all, some, most, few, etc. which indicate the number of
Quantifier_(logic)
Statement that is true regardless of the truth or falsity of its constituent propositions
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth
Logical_truth
Number of arguments required by a function
In logic, mathematics, and computer science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics
Arity
Set of sentences in a formal language
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first
Theory_(mathematical_logic)
Properties linking logical conjunction and disjunction
In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, also called the duality principle. It is the most
Conjunction/disjunction duality
Conjunction/disjunction_duality
Subfield of automated reasoning and mathematical logic
automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated
Automated_theorem_proving
Argument in philosophical logic
1996) proceeds as follows. Assumptions: Substitution. If two terms designate the same thing, then substituting one for another in a sentence does not change
Slingshot_argument
Reasoning for mathematical statements
frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language that usually
Mathematical_proof
Theory of logic to account for observations from quantum theory
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions
Quantum_logic
Axioms for the natural numbers
In mathematical logic, the Peano axioms (/piˈɑːnoʊ/; [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural
Peano_axioms
American scientist (1839–1914)
contributions to logic, such as theories of relations and quantification. C. I. Lewis wrote, "The contributions of C. S. Peirce to symbolic logic are more numerous
Charles_Sanders_Peirce
Postulation about the significance of Christ's death
Penal substitution, also called penal substitutionary atonement and especially in older writings forensic theory, is a theory of the atonement within Protestant
Penal_substitution
Mathematical use of "for all"
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every"
Universal_quantification
Sequence of words formed by specific rules
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
Formal_language
Schrödinger logics are a kind of non-classical logic in which the law of identity is restricted. These logics are motivated by the consideration that
Schrödinger_logic
SUBSTITUTION LOGIC
SUBSTITUTION LOGIC
Boy/Male
Tamil
Intelligent, Logical
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Gujarati, Hindu, Indian, Kannada, Tamil
Trick; Power; Strategy; Solution by Logic; By Reasoning
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Female
English
 This English name is usually chosen for its association with the butterfly genus. Its origin remains uncertain despite the claim that it was invented by Jonathan Swift, author of Gulliver's Travels, for his intimate friend Esther Vanhomrigh. Supposedly he created it by combining the first syllable of her surname, Van-, with her first name, Esther, or the suffix -essa; but, if he created it at all, it is more likely that he based it on the Greek name Phanessa, substituting the "Ph" with the "V" from Esther's surname. Besides, the name may have existed before Swift's time. Phanessa is a feminine form of Orphic Phanes, the name of a primeval, hermaphroditic golden-winged god, VANESSA means "bring to light; make appear."Â
Surname or Lastname
English
English : from the medieval personal name Hicke, a pet form of Richard. The substitution of H- as the initial resulted from the inability of the English to cope with the velar Norman R-.Dutch : from a pet form of a Germanic personal name, such as Icco or Hikke (a Frisian derivative of a compound name with the first element hild ‘strife’, ‘battle’).East German : from a derivative of a Slavic pet form of Heinrich.South German : from Hiko, a pet form of any of the Germanic personal names formed with hild ‘strife’, ‘battle’ as the first element.
Boy/Male
Tamil
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Arabic, Muslim, Pashtun
Logic; Reason
Girl/Female
Hindu
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Indian
Successful; Logical Thinkers
Boy/Male
Hindu
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Boy/Male
Indian
Intelligent, Logical
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Girl/Female
Tamil
Viviktha | விவீகà¯à®¤à®¾Â
Distinguished, Pure, Deep, Logically intelligent
Viviktha | விவீகà¯à®¤à®¾Â
Girl/Female
Tamil
Vivikta | விவிகதா
Distinguished, Pure, Deep, Logically intelligent
Vivikta | விவிகதா
Girl/Female
Bengali, Hindu, Indian, Tamil, Telugu
Logically Intelligent; Who Stands Alone
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Boy/Male
Tamil
Love and kindness, Analytical, Logical
Girl/Female
Danish, Hindu, Indian, Japanese
Ray of Light; Logical
SUBSTITUTION LOGIC
SUBSTITUTION LOGIC
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from a place in West Yorkshire, so named from an unattested Old English element henge ‘steep’ + Old English clif ‘cliff’.
Girl/Female
Muslim
Decoration. Beauty.
Girl/Female
Indian
Candle, Light
Boy/Male
French
Eagle wolf.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Radha and Krishna
Girl/Female
Australian, Hawaiian, Hebrew
A Fawn; A Bird
Boy/Male
Biblical
Testimony of the assembly.
Boy/Male
Tamil
Arumugam | à®…à®°à¯à®®à¯à®•à®®
Murugan
Female
Ukrainian
, queen.
Boy/Male
Finnish
Stone.
SUBSTITUTION LOGIC
SUBSTITUTION LOGIC
SUBSTITUTION LOGIC
SUBSTITUTION LOGIC
SUBSTITUTION LOGIC
n.
A hypothetical radical derived from ammonium by the substitution of metallic atoms in place of hydrogen.
a.
Having or exercising delegated power; acting by substitution, or in the place of another.
a.
Substituting on leaves; leaf-eating.
a.
Admitting of exchange or mutual substitution.
a.
Tending to afford or furnish a substitute; making substitution; capable of being substituted.
n.
The office or authority of one acting for another; delegated authority.
n.
The doctrine that Christ suffered vicariously, being substituted for the sinner, and that his sufferings were expiatory.
n.
The act of substituting or putting one person or thing in the place of another; as, the substitution of an agent, attorney, or representative to act for one in his absense; the substitution of bank notes for gold and silver as a circulating medium.
a.
Having five hydrogen atoms capable of substitution.
n.
The state of being substituted for another.
a.
Of or pertaining to substitution; standing in the place of another; substituted.
n.
The designation of a person in a will to take a devise or legacy, either on failure of a former devisee or legatee by incapacity or unwillingness to accept, or after him.
n.
The act or process of substituting an atom or radical for another atom or radical; metethesis; also, the state of being so substituted. See Metathesis.
p. pr. & vb. n.
of Substitute
n.
removal of things from one place to another; substitution of one thing for another.
a.
Of or pertaining to substitution; substitutional.
a.
Containing substitutions or replacements; having been subjected to the process of substitution, or having some of its parts replaced; as, alcohol is a substituted water; methyl amine is a substituted ammonia.
a.
Having or exercising delegated power; acting by substitution, or in the place of another.
n.
Exchange; replacement; substitution; metathesis.
v. i.
To obtain or bargain for exemption or substitution; to effect a commutation.